Mathematics · Foundation · Counting Objects to 10 · Term 1

Number Names and Numerals to 10

Students extend their understanding of numbers to include rational numbers, representing them as fractions.

• ACARA Content Descriptions
• AC9M6N01
• AC9M6N02

About This Topic

Ordering and Comparing introduces students to the relative nature of numbers. It moves beyond identifying a single quantity to understanding how that quantity sits in relation to others using terms like 'more', 'less', 'fewer', and 'the same'. Under the ACARA framework, students learn to compare collections and order them from smallest to largest, which is a precursor to understanding the number line and place value.

This topic is highly visual and tactile. Students need to see groups side-by-side to make sense of 'more' and 'less'. In an Australian classroom, this is a great time to use local flora or images of Australian animals to make comparisons, such as comparing the number of cockatoos to the number of galahs in a picture. Students grasp this concept faster through structured discussion and peer explanation where they have to justify why one group is larger than another.

Key Questions

1. Can you point to the numeral that shows how many apples are in this picture?
2. What does the numeral 7 look like , can you draw it?
3. How do we say the name of this number?

Learning Objectives

• Identify the numeral that represents a given quantity of objects up to 10.
• Write the numeral that corresponds to a spoken number name from one to ten.
• Compare two groups of objects up to 10 and identify which group has more, less, or the same amount.
• Explain the meaning of a numeral by representing it with a collection of objects.

Before You Start

One-to-One Correspondence

Why: Students need to be able to match each object in a set with one number word or numeral to count accurately.

Key Vocabulary

Numeral	A symbol used to represent a number, such as 1, 2, or 3.
Count	To say numbers in order and determine the total number of items in a set.
More	A greater quantity or number.
Less	A smaller quantity or number.
Same	Equal in number or amount.

Watch Out for These Misconceptions

Common Misconception

Students confuse 'more' with 'bigger' in terms of physical size.

What to Teach Instead

Show a group of two large blocks next to five small beads. Ask which group has 'more'. Use peer discussion to clarify that 'more' refers to the count of items, not the space they occupy.

Common Misconception

Students struggle with the concept of 'less' compared to 'more'.

What to Teach Instead

The term 'less' is often less familiar than 'more'. Use hands-on modeling where students physically remove items from a group to see the quantity decrease, reinforcing the vocabulary through action.

Active Learning Ideas

Inquiry Circle: The Human Number Line

Give each student a card with a number or a set of dots. Without speaking, students must organise themselves into a line from the smallest quantity to the largest by showing their cards to one another and finding their place.

20 min·Whole Class

Stations Rotation: More or Less Jars

Set up jars filled with different amounts of pasta or buttons. At each station, students work in pairs to pick two jars and use 'more' and 'less' cards to label them, then record their findings by drawing the jars in order.

25 min·Small Groups

Think-Pair-Share: Is it Fair?

Show two unequal groups of 'treats' (like stickers). Ask students if the groups are equal. Students think about how to make them equal, share their idea with a partner, and then suggest a solution to the class, such as moving items from the larger group to the smaller one.

15 min·Pairs

Real-World Connections

• When shopping at a local Australian farmers market, children can count the number of fruits or vegetables available, comparing quantities to decide which stall has more apples or fewer oranges.
• Early childhood educators use counting and numeral recognition daily when setting up play areas, organizing resources, and managing snack times for groups of children.

Assessment Ideas

Quick Check

Present a collection of 5-8 objects (e.g., toy kangaroos). Ask students: 'How many kangaroos are there?' Then, show them three numeral cards (e.g., 5, 7, 9) and ask: 'Which card shows how many kangaroos we have?'

Discussion Prompt

Show two different groups of familiar objects, like shells or blocks, with quantities up to 10. Ask students: 'Which group has more shells? How do you know?' Encourage them to explain their reasoning using counting or visual comparison.

Exit Ticket

Give each student a small card with a numeral (e.g., 4 or 6). Ask them to draw that many dots or objects on the back of the card to represent the numeral.

Frequently Asked Questions

What vocabulary should I use for comparing numbers?

Focus on 'more than', 'less than', 'fewer than', 'equal to', and 'the same as'. Using 'fewer' for countable objects (like apples) and 'less' for continuous amounts (like water) is technically correct, but at the Foundation level, the priority is understanding the concept of relative quantity.

How can I help my child understand the order of numbers?

Use everyday opportunities like climbing stairs or setting the table. Ask, 'We have three plates, do we need more or fewer to have five?' Use a visual number line at home so they can see that as we move to the right, the numbers always represent more.

How can active learning help students understand comparing?

Active learning, such as 'The Human Number Line', forces students to physically position themselves in relation to others. This spatial experience helps cement the idea of sequence. When students work in pairs to compare jars, they must use mathematical language to negotiate and agree, which builds their fluency and confidence more effectively than solo work.

Why is 'the same as' an important concept?

Understanding equality is the foundation for algebra. It is not just about one group being bigger; it is about recognising when two different-looking sets (like four dots in a square and four dots in a line) represent the same quantity. This is known as conservation of number.